Integration of Kaluza-Klein modes in Yang-Mills theories

A five-dimensional pure Yang-Mills theory, with the fifth coordinate compactified on the orbifold S1/Z2 of radius R, leads to a four-dimensional theory which is governed by two types of infinitesimal gauge transformations, namely, the well-known standard gauge transformations (SGT) dictated by the SU4(N) group under which the zero Fourier modes Aμ(0)a transform as gauge fields, and a set of nonstandard gauge transformations (NSGT) determining the gauge nature of the Kaluza-Klein (KK) excitations Aμ(m)a. By using a SGT-covariant gauge-fixing procedure for removing the degeneration associated with the NSGT, we integrate out the KK excitations and obtain a low-energy effective Lagrangian expansion involving all of the independent canonical-dimension-six operators that are invariant under the SGT of the SU4(N) group and that are constituted by light gauge fields, Aμ(0)a, exclusively. It is shown that this effective Lagrangian is invariant under the SGT, but it depends on the gauge-fixing of the gauge KK excitations. Our result shows explicitly that the one-loop contributions of the KK excitations to light (standard) Green's functions are renormalizable.